An efficient model for modelling Barkhausen noise in PMA thin films

The motion of domain walls in thin films with perpendicular magnetic
anisotropy (PMA) is of great interest due to their technological applications
in spintronic devices, as well as the critical phenomenon of Barkhausen noise
due to the domain wall pinning to quenched disorder. However, current
numerical studies of domain walls, using micromagnetic discretized solvers on
the entire system, are limited to small system sizes by the expensive
computation of the far-field forces between every pair of spins. As a result,
the statistical signature of Barkhausen noise has strong finite size effects in
such studies.

We present an efficient, principled numerical model which reduces the
description of the PMA thin film to a single one-dimensional domain wall, by
integrating over the coordinate perpendicular to the domain wall. The full
nonlocal demagnetizing field is included in the computation, but formulated as
a an integral over the remaining dimension along the wall. This allows for
numerical studies of Barkhausen noise in large systems, while still including
physical effects such as Walker breakdown and nonlocal interactions.